Elliptic curve isogeny class 20956.6-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20956.6-c
• Conductor: 20956.6
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 20956.6-c over \(\Q(\sqrt{-3}) \)

Isogeny class 20956.6-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
20956.6-c1	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 13496 a - 15653\) , \( 772288 a - 509794\bigr] \)
20956.6-c2	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -4 a - 3\) , \( 8 a - 4\bigr] \)
20956.6-c3	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -149 a + 187\) , \( -322 a + 510\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)

Isogeny graph